1. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Chapter 15 2 k Factorial Experiments and Fractions

2. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.1 Introduction

3. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.2 The 2 k Factorial: Calculation of Effects and Analysis of Variance

4. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 4 Table 15.1 A 2 2 Factorial Experiment

5. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 5 Figure 15.1 Response suggesting apparent interaction

6. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 6 Table 15.2 2 2 Factorial with No Interaction

7. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 7 Table 15.3 2 2 Factorial with Interaction

8. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 8 Figure 15.2 Interaction plot for data of Table 15.2

9. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 9 Figure 15.3 Interaction plot for data of Table15.3

10. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 10 Table 15.4 Signs for Contrasts in a 2 2 Factorial Experiments

11. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 11 Table 15.5 Signs for Contrasts in a 2 3 Factorial Experiment

12. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 12 Figure 15.4 Geometric view of 2 3

13. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.3 Nonreplicated 2 k Factorial Experiment

14. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 14 Table 15.6 Data for Case Study 15.1

15. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 15 Figure 15.5 Normal quantile-quantile plot of effects for Case Study 15.1

16. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 16 Table 15.7 Illustration of Two- Factor Interaction

17. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 17 Figure 15.6 Interaction plot for Case Study 15.1

18. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 18 Figure 15.7 SAS printout for data of Case Study 15.1

19. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 19 Figure 15.8 ANOVA table for Exercise 15.3

20. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.4 Factorial Experiments in a Regression Setting

21. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 21 Table 15.8 Data for Example 15.2

22. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 22 Figure 15.9 SAS printout for data of Case Study 15.2 continued on next slide

23. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 23 Figure 15.9 SAS printout for data of Case Study 15.2 (cont’d)

24. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.5 The Orthogonal Design

25. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 25 Figure 15.10a Geometric presentation of contrast for the 23 factorial design continued on next slide

26. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 26 Figure 15.10b Geometric presentation of contrast for the 23 factorial design (cont’d) continued on next slide

27. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 27 Figure 15.10c Geometric presentation of contrast for the 23 factorial design (cont’d)

28. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 28 Figure 15.11 A 2 2 design with center runs

29. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 29 Figure 15.12 2 2 factorial with 5 center runs

30. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 30 Figure 15.13 2 2 factorial with runs at (0,0)

31. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 31 Figure 15.14 Graph Exercise 15.17

32. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.6 Fractional Factorial Experiments

33. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 33 Table 15.9 Contrasts for the Seven Available Effects for a 2 3 Factorial Experiment

34. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 34 Figure 15.15 The fractions of the 2 3 factorial

35. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 35 Table 15.10 Construction of the Two 2 3 -1 Designs

36. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 36 Table 15.11 Construction of the Two 2 4-1 Designs

37. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 37 Table 15.12 A 2 6-2 Design

38. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.7 Analysis of Fractional Factorial Experiments

39. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 39 Table 15.13 Signs for Contrasts in a Half- Replicate of a 2 3 Factorial Experiments

40. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 40 Table 15.14 Data for Example 15.6

41. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 41 Table 15.15 Analysis of Variance for the Data of a Half-Replicate of a 2 5 Factorial Experiment

42. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.8 Higher Fractions and Screening Designs

43. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 43 Definition 15.1

44. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.9 Construction of Resolution III and IV Designs with 8,16,and 32 Design Points

45. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 45 Table 15.16 Some Resolution III, IV, V, VI and VII 2 k-p Designs

46. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.10 Other Two-Level Resolutions III Designs; The Plackett-Burman Designs

47. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.11 Introduction to Response Surface Methodology

48. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 48 Table 15.17 Central Composite Design for Example 15.8

49. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 49 Figure 15.16 Central composite design for Example 15.8

50. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 50 Figure 15.17 Plot for the response surface prediction conversion for Example 15.8

51. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 51 Figure 15.18 Contour plot of predicted conversion for Example 15.8

52. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Section 15.12 Robust Parameter Design

53. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 53 Definition 15.2

54. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 54 Table 15.18 Design for Example 15.9

55. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 55 Table 15.19 Control Factors for Case Study 15.3

56. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 56 Table 15.20 Noise Factors for Case Study 15.3

57. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 57 Table 15.21 Crossed Arrays and Response Values for Case Study 15.3

58. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 58 Figure 15.19 Plot showing the influence of factors on the mean response

59. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 59 Figure 15.20 Mean and standard deviation for Case Study 15.4

60. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 60 Table 15.22 Experimental Data in a Crossed Array

61. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 61 Figure 15.21 Interaction plots for the data in Table 15.22

62. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15 - 62 Figure 15.22 Interaction plots for the data in Exercise 15.31

63. Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Potential Misconceptions and Hazards; Relationship to Material in Other Chapters Section 15.13